Question

Which of the following is the third term of the expansion (a + b) n ?

C(n, 2)a^(n-2) - b^2
C(n, 3)a^(n-3) - b
C(n, 2)a^2 - b^(n - 2)

Answer 1

The third term of the expansion
`(a+b)^n` is
`C(n,2)\cdot a^(n-2)\cdot b^(2)`.

Explanation:

According to the binomial expansion,

`(a+b)^n=C(n,0)a^(n)+C(n,1)a^(n-1)b+...+C(n,n)b^n`

So, the rth term of this expansion is

`C(n,r-1)a^(n-r+1)b^((r-1))`

We have to find the third term of the expansion
`(a+b)^n` is

`C(n,3-1)a^(n-3+1)b^((3-1))`

`C(n,2)\cdot a^(n-2)\cdot b^(2)`

Therefore the third term of the expansion
`(a+b)^n` is
`C(n,2)\cdot a^(n-2)\cdot b^(2)`.